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On the Decay Rates of Porous Elastic Systems

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Abstract

In this paper we analyze the porous elastic system. We show that viscoelasticity is not strong enough to make the solutions decay in an exponential way, independently of any relationship between the coefficients of wave propagation speed. However, it decays polynomially with optimal rate. When the porous damping is coupled with microtemperatures, we give an explicit characterization on the decay rate that can be exponential or polynomial type, depending on the relation between the coefficients of wave propagation speed. Numerical experiments using finite differences are given to confirm our analytical results. It is worth noting that the result obtained here is different from all existing in the literature for porous elastic materials, where the sum of the two slow decay processes determine a process that decay exponentially.

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Acknowledgements

The first author has been partially supported by the CNPq Grant 163428/2014-0. The second author thanks to PNPD/CAPES for his financial support. The third author has been partially supported by the CNPq Grant 311553/2013-3 and CNPq Grant 458866/2014-8 (Universal-2014).

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  1. Mathematics faculty, Federal University of Pará, Augusto Corrêa Street, Number 01, 66075-110, Belém, PA, Brazil

    M. L. Santos, A. D. S. Campelo & D. S. Almeida Júnior

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  1. M. L. Santos
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  2. A. D. S. Campelo
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  3. D. S. Almeida Júnior
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Correspondence to A. D. S. Campelo.

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Santos, M.L., Campelo, A.D.S. & Almeida Júnior, D.S. On the Decay Rates of Porous Elastic Systems. J Elast 127, 79–101 (2017). https://doi.org/10.1007/s10659-016-9597-y

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